The particle-in-cell code EPOCH was extended to include field and collisional ionisation\ud for use in simulating initially neutral or partially-ionised targets in laser-plasma inter-\ud actions. The means by which particles ionise in the the field of an intense laser was\ud described and physical models were included to determine the instantaneous ionisa-\ud tion rate at particles within the simulation domain for multiphoton, tunnelling, barrier-\ud suppression and electron-impact ionisation. The algorithms used to implement these\ud models were presented and demonstrated to produce the correct ionisation statistics. A\ud scheme allowing for modelling small amounts of ionisation for an arbitrarily low number\ud of superparticles was also presented for comparison and it was shown that for sufficient\ud simulation time the two schemes converge. The three major mechanisms of ionisation\ud in laser-plasma interactions were described as being ionisation-induced defocussing, fast\ud shuttering and ionisation injection. Simulations for these three effects were presented\ud and shown to be in good agreement with theory and experiment. For fast-shuttering,\ud plasma mirrors were simulated using the pulse profile for the Astra Gemini laser at the\ud Central Laser Facility. Rapid switch-on and the theoretical maximum for contrast ratio\ud was observed. For ionisation injection, simulations for laser wakefield acceleration in a\ud helium gas were performed and the accelerated electron population was shown to be\ud greatly increased through use of a 1% nitrogen dopant consistent with the experimental\ud results of McGuffey et al. A study of the laser filamentation instability due to SRS\ud backscatter at the relativistically corrected quarter critical surface (RCQCS) was per-\ud formed in collaboration with C.S. Brady and T.D. Arber at the University of Warwick\ud [1]. It was found that for hydrogen and plastic the instability was unaffected by the in-\ud clusion of ionisation. Further study with argon revealed a \ud attening of the RCQCS and\ud it was demonstrated that for a material with multiple ionisation levels ionising strongly\ud near the self-focussed intensities at the RCQCS, rapid ionisation caused an inversion of\ud the RCQCS that suppressed the filamentation instability.